The Reality of eDate: 7/26/96 at 15:52:31 From: Anonymous Subject: The Reality of e Ok, so e can be defined as a limit or as a sum. Does it exist outside of the classroom? Can I find it in nature? Date: 7/26/96 at 22:7:23 From: Doctor Paul Subject: The Reality of e A couple of things come to mind. The first is the use of the function e^x to model population growth and population decay. P(t) = Po e^(-kt) where P(t) is the population at time t, Po is the population at t = 0 and k is decay (or growth) constant. It can be used to solve problems of this sort: This same model can be used to compute interest on a bank account, compounded continuously. Another use of the e^x function is in modeling simple harmonic motion (using differential equations). It could model underdamped, overdamped, or critically-damped motion. Yet another use of the e^x function is in the building of catenaries (like the arc in St. Louis). A catenary is the curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force. y(t) = 1/2*(e^t + e^(-t)) Finally, a form of e^(-x^2) is used in Statistics. The curve: f(x) = e^(-.5*x^2) ----------- sqrt(2*Pi) What's so special about this curve? The area under it is equal to one. That's right: the integral of f(x) from -infinity to infinity is 1. This works out really nicely. The curve is most commonly referred to as a bell curve and is often used for curving tests in college. -Doctor Paul, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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